Response Characteristics of the Nagumo Neuron Model to the 1/f-like Fluctuated Pulse Inputs

Abstract

Responses of the Nagumo neural circuit to nonperiodic pulse-train stimulation are studied in detail. In particular, using the input pulses with the 1/f-like fluctuation, we show the global firing structure. To try to clarify the role of the 1/f fluctuation in the neural information processing, we investigate the histogram of the neuron-response interval, the power spectral density for neuron responses, and the return map of the membrane potential. As numerical results, it is shown that the almost same global firing pattern structure as one for periodic pulse stimulations. Four observations, furthermore, are obtained as follows : (1) there are three kinds of characteristic spectrals of neuron responses, (2) all responses for the 1/fn spectral inputs in the single-response region have the 1/f2-like spectral, (3) characteristics of neuron responses are independent of the fluctuation- width of inputs, and (4) in the non 1/f random spectral inputs, the response spectral has the almost exponential type.